At the daily Downing Street briefing, he said: “At least to date the evidence has been that we wouldn’t be able to open up all schools without a very real risk that the R rate – the transmission rate – would rise at such a level that we would risk a second spike.

“We have asked Sage for the options on this and we will, as ever, continue to be guided by the scientific advice we get.”

In the Commons, Mr WIlliamson said he wants to see children returning to school “when it’s the right time” based on the scientific and medical advice.

“We will take a phased approach in terms of reopening schools and we will always aim to give schools, parents and, of course, critically importantly, children the maximum notice in terms of when this is going to happen,” he said.

He was challenged by shadow education secretary Rebecca Long-Bailey about the Government’s plans for reopening schools.

She warned that parents are “anxious” about sending their children back to class.

In her first outing at the despatch box in her new role, Ms Long-Bailey said: “Constant speculation on when schools will reopen and whether it is safe to do so is leaving many parents, pupils and staff anxious.”

Tory MP and chairman of the Education Select Committee Robert Halfon suggested the Government should offer a “catch-up premium with tuition, mentoring and wellbeing” for students as schools start to reopen.

Mr Williamson said that ensuring every child has the ability to catch up with their studies is something his department is “working at very closely” and that he was “very interested” in Mr Halfon’s idea.

We will take a phased approach in terms of reopening schools and we will always aim to give schools, parents and, of course, critically importantly, children the maximum notice in terms of when this is going to happenGavin Williamson

Minister for children and families Vicky Ford announced that parents who are normally eligible for the Government’s free childcare will continue to be eligible for those entitlements during the summer term even if their income levels have changed.

Labour’s Steve McCabe (Birmingham, Selly Oak) said: “Nurseries and childcare providers have struggled to stay open during this crisis and the minister will know that the confusion over the DfE’s (Department for Education) statements on free entitlement and the furlough scheme has caused a lot of financial headaches.”

Ms Ford replied: “We will always make sure early years providers get the best support possible.”

She added: “A new announcement for parents: Parents who are normally eligible for the Government’s free childcare will continue to be eligible for those entitlements during this summer term even if their income levels have changed due to the virus and this will be a massive support to families as well as to providers.”

In response to a request from Tory Steve Double (St Austell and Newquay), education minister Gillian Keegan also announced that new hospitality and tourism-related T-Levels will be introduced to help these sectors recover after the pandemic.

“To support both tourism and hospitality, which I know are important to his constituency, we will offer T-Levels in cultural heritage and visitor attraction, catering and management administration,” Ms Keegan said.